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A326310
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Arithmetic numbers (A003601) that are not RMS numbers (A140480).
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1
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3, 5, 6, 11, 13, 14, 15, 17, 19, 20, 21, 22, 23, 27, 29, 30, 31, 33, 35, 37, 38, 39, 42, 43, 44, 45, 46, 47, 49, 51, 53, 54, 55, 56, 57, 59, 60, 61, 62, 65, 66, 67, 68, 69, 70, 71, 73, 77, 78, 79, 83, 85, 86, 87, 89, 91, 92, 93, 94, 95, 96, 97, 99, 101, 102
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OFFSET
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1,1
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COMMENTS
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Numbers m such that the arithmetic mean of the divisors of m is an integer but the quadratic mean (the root mean square) of the divisors of m is not an integer.
Corresponding values of A(m): 2, 3, 3, 6, 7, 6, 6, 9, 10, 7, 8, 9, 12, 10, 15, 9, 16, 12, 12, 19, 15, 14, 12, 22, 14, 13, 18, ...
Corresponding values of Q(m): sqrt(5), sqrt(13), sqrt(25/2), sqrt(61), sqrt(85), sqrt(125/2), sqrt(65), sqrt(145), sqrt(181), ...
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LINKS
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MATHEMATICA
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Select[Range[120], IntegerQ[Mean[Divisors[#]]]&&!IntegerQ[RootMeanSquare[ Divisors[ #]]]&] (* Harvey P. Dale, Mar 04 2023 *)
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PROG
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(Magma) [m: m in [1..10^6] | IsIntegral(SumOfDivisors(m) / NumberOfDivisors(m)) and not IsIntegral(Sqrt(&+[d^2: d in Divisors(m)] / NumberOfDivisors(m)))]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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